IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v16y2001i4d10.1007_s180-001-8329-3.html
   My bibliography  Save this article

Computing the Standards Errors of Mixture Model Parameters with EM when Classes are Well Separated

Author

Listed:
  • Michel Wedel

    (University of Groningen
    The University of Michigan Business School)

Abstract

Summary It is shown that for finite mixtures the missing information tends to zero as the number of observations on each subject increases. Then, the classes become perfectly separated (i.e. the posterior membership probabilities are close to 0 or 1), the observed information tends to the complete information and the class-specific parameters in the mixture model become information orthogonal across classes. Then the asymptotic standard errors of parameter estimates can be obtained directly from the EM algorithm. The degree of class-separation is derived for which the amount of missing observation is approximately negligible and the asymptotic standard errors based on the complete information matrix are sufficiently accurate. Empirical illustrations are provided. A Monte Carlo study is performed to examine the extent to which the approximation is adequate. A comparison is made with other methods to approximate the observed information matrix. It is concluded that if the entropy of the posterior probabilities is larger than 0.95 the proposed approximation is reasonably accurate.

Suggested Citation

  • Michel Wedel, 2001. "Computing the Standards Errors of Mixture Model Parameters with EM when Classes are Well Separated," Computational Statistics, Springer, vol. 16(4), pages 539-558, December.
    • Handle: RePEc:spr:compst:v:16:y:2001:i:4:d:10.1007_s180-001-8329-3
    DOI: 10.1007/s180-001-8329-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s180-001-8329-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s180-001-8329-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    2. Wedel, Michel & DeSarbo, Wayne S, 1996. "An Exponential-Family Multidimensional Scaling Mixture Methodology," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 447-459, October.
    3. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    4. Conor Dolan & Han Maas, 1998. "Fitting multivariage normal finite mixtures subject to structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 227-253, September.
    5. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ana Oliveira-Brochado & Francisco Vitorino Martins, 2014. "Identifying Small Market Segments with Mixture Regression Models," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 4(4), pages 812-812.
    2. Wayne S. DeSarbo & Alexandru M. Degeratu & Michel Wedel & M. Kim Saxton, 2001. "The Spatial Representation of Market Information," Marketing Science, INFORMS, vol. 20(4), pages 426-441, June.
    3. David F. Larcker & Scott A. Richardson, 2004. "Fees Paid to Audit Firms, Accrual Choices, and Corporate Governance," Journal of Accounting Research, John Wiley & Sons, Ltd., vol. 42(3), pages 625-658, June.
    4. Ana Oliveira-Brochado & Francisco Vitorino Martins, 2008. "Determining the Number of Market Segments Using an Experimental Design," FEP Working Papers 263, Universidade do Porto, Faculdade de Economia do Porto.
    5. Pennings, Joost M. E. & Garcia, Philip, 2004. "Hedging behavior in small and medium-sized enterprises: The role of unobserved heterogeneity," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 951-978, May.
    6. Pennings, Joost M.E. & Garcia, Philip & Irwin, Scott H. & Good, Darrel L., 2003. "How To Group Market Participants? Heterogeneity In Hedging Behavior," 2003 Annual meeting, July 27-30, Montreal, Canada 21963, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. Heungsun Hwang & Marc Tomiuk, 2010. "Fuzzy clusterwise quasi-likelihood generalized linear models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 255-270, December.
    8. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    9. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    10. Khalique, Abdul & Wang, Yichen & Ahmed, Khalid, 2025. "Europe's environmental dichotomy: The impact of regulations, climate investments, and renewable energy on carbon mitigation in the EU-22," Energy Policy, Elsevier, vol. 198(C).
    11. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    12. Chen, Cathy W.S. & Chan, Jennifer S.K. & So, Mike K.P. & Lee, Kevin K.M., 2011. "Classification in segmented regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2276-2287, July.
    13. Martínez-Zarzoso, Inmaculada & Maruotti, Antonello, 2011. "The impact of urbanization on CO2 emissions: Evidence from developing countries," Ecological Economics, Elsevier, vol. 70(7), pages 1344-1353, May.
    14. Réal Carbonneau & Gilles Caporossi & Pierre Hansen, 2014. "Globally Optimal Clusterwise Regression By Column Generation Enhanced with Heuristics, Sequencing and Ending Subset Optimization," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 219-241, July.
    15. Grewal, Rajdeep & Chakravarty, Anindita & Ding, Min & Liechty, John, 2008. "Counting chickens before the eggs hatch: Associating new product development portfolios with shareholder expectations in the pharmaceutical sector," International Journal of Research in Marketing, Elsevier, vol. 25(4), pages 261-272.
    16. repec:jss:jstsof:11:i08 is not listed on IDEAS
    17. Allen, Eric J. & Larson, Chad R. & Sloan, Richard G., 2013. "Accrual reversals, earnings and stock returns," Journal of Accounting and Economics, Elsevier, vol. 56(1), pages 113-129.
    18. M. Wedel & W. S. Desarbo & J. R. Bult & V. Ramaswamy, 1993. "A latent class poisson regression model for heterogeneous count data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 397-411, October.
    19. Michele Battisti & Filippo Belloc & Massimo Del Gatto, 2015. "Unbundling Technology Adoption and tfp at the Firm Level: Do Intangibles Matter?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(2), pages 390-414, June.
    20. Wedel, Michel & DeSarbo, Wayne S., 1996. "Semiparametric estimation of (constrained) ultrametric trees," Research Report 96B34, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    21. Ana Oliveira-Brochado & Francisco Vitorino Martins, 2008. "Segmentação de Mercado e modelos mistura de regressão para variáveis normais," FEP Working Papers 262, Universidade do Porto, Faculdade de Economia do Porto.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:16:y:2001:i:4:d:10.1007_s180-001-8329-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.